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Chapter 39: Q.51 (page 1140)

Consider the electron wave function

ψx=cxx≤1nmcxx≤1nm

where x is in nm. a. Determine the normalization constant c.

b. Draw a graph of c1x2 over the interval -5 nm … x … 5 nm. Provide numerical scales on both axes.

c. Draw a graph of 0 c1x2 0 2 over the interval -5 nm … x … 5 nm. Provide numerical scales.

d. If 106 electrons are detected, how many will be in the interval -1.0 nm … x … 1.0 nm?

Short Answer

Expert verified

The wave function of the electronψx=cxx≤1nmcxx≤1nm

Step by step solution

01

The probability independent

∫-∞+∞ψxdx=1∫-∞+∞ψxdx+∫-11ψxdx+∫12ψxdx=1∫-∞+∞cx2dx+∫-11cxdx+∫12cx2dx=1c2223=1

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Most popular questions from this chapter

Consider the electron wave function

ψX=0x<0nm1.414nm-12e-x1.0nmx≥0nm

where x is in cm.

a. Determine the normalization constant c.

b. Draw a graph of c1x2 over the interval -2 cm ≤x ≤2 cm. Provide numerical scales on both axes.

c. Draw a graph of 0 c1x2 0 2 over the interval -2 cm ≤x ≤2 cm. Provide numerical scales.

d. If 104 electrons are detected, how many will be in the interval 0.00 cm ≤x ≤0.50 cm?

shows the probability density for finding a particle at position x. a. Determine the value of the constant a, as defined in the figure. b. At what value of x are you most likely to find the particle? Explain. c. Within what range of positions centered on your answer to part b are you 75% certain of finding the particle? d. Interpret your answer to part c by drawing the probability density graph and shading the appropriate region.

FIGURE EX39.13 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010−mm-wide strip at (a) x=0.000mm, (b)x=0.500mm, (c) x=1.000mm, and (d) x=2.000mm?

The probability density for an electron that has passed through an experimental apparatus. If 1.0×106electrons are used, what is the expected number that will land in alocalid="1649312933417" 0.010mmwide strip atlocalid="1649312941736" (a)x=0.000mmand localid="1649312949893" (b)2.000mm?

Consider the electron wave function

ψX=csin2πxL0≤x≤L0x<0orx>L

a. Determine the normalization constant c. Your answer will be in terms of L.

b. Draw a graph of ψxover the interval -L≤x ≤2L.

c. Draw a graph of ψx2over the interval -L ≤x ≤2L. d. What is the probability that an electron is in the interval 0 ≤x ≤L/3?

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